ClockLFSR (Linear Feedback Shift Register)

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ClockLFSR (Linear Feedback Shift Register)

Symbol

Available in ADS

Parameters

Name	Description	Units	Default
Vlow	Lower threshold voltage	V	0.25
Vhigh	Upper threshold voltage	V	0.75
Taps	Bits used to generate feedback	None	bin("10000100")
Seed	Initial value loaded into shift register	None	bin("10101010")
Rout	Output resistance	Ohm	1

Notes/Equations

ClockLFSR can be used to generate PN sequences with user-defined recurrence relations. The input is a clock signal; with each positive clock edge, the next output bit is calculated. A clock edge occurs any time the baseband input signal rises through 0.5V.
This model works in transient and circuit envelope simulation.
With each positive clock edge, data is shifted to the right in the shift register. The length of the shift register is determined by the most significant one-bit in the Taps value.

LFSR Model

The numbers a(1), a(2), ... , a(r) are the binary feedback coefficients and are specified by the Taps parameter. This value may be specified as a decimal number, or as a binary pattern if the bin( ) function is used. The initial contents of the shift are specified by the value of the Seed parameter. The following equations describe the operation of this component:
At each positive clock edge n (n ≥ 1),
for n ≥ 1:

where
D(0) = Seed₂ (0)
D(−1) = Seed₂ (1)
.
.
.
D(1−r) = Seed₂ (r−1)
and Seed =

where Seed₂(k) Œ{0,1} for 0 ≤ k < r.
Example: Let Seed = 2, and Taps = 7
then
Seed₂ (0) = 0
Seed₂ (1) = 1
.
.
.
Seed₂ (6) = 0
thus,
(0) = Seed2 (0) = 0
D(-1) = Seed2 (1) = 1
D(-2) = Seed2 (2) = 0
.
.
.
D(-6) = Seed₂₂ (6) = 0
Seed2 (2) = 0
Linear Feedback Shift Register ClockLFSR
The binary feedback coefficients are specified by Taps. For example, the recurrence relation
D(n) = (D(n-7) + D(n-3) + D(n-2) + D(n-1))mod 2
is specified by:
Taps = bin("1000111")
or
Taps = 71
The following table provides a list of feedback coefficients for linear feedback shift registers showing one or more alternate feedback connections for a given number of stages.

Feedback Connections for Linear m-Sequences*

No. of Stages	Code Length	Maximal Taps
2	3	[2, 1]
3	7	[3, 1]
4	15	[4, 1]
5	31	[5, 2] [5, 4, 3, 2] [5, 4, 2, 1]
6	63	[6, 1] [6, 5, 2, 1,] [6, 5, 3, 2,]
7	127	[7, 1] [7, 3] [7, 3, 2, 1,] [7, 4, 3, 2,] [7, 6, 4, 2] [7, 6, 3, 1] [7, 6, 5, 2] [7, 6, 5, 4, 2, 1] [7, 5, 4, 3, 2, 1]
8	255	[8, 4, 3, 2] [8, 6, 5, 3] [8, 6, 5, 2] [8, 5, 3, 1] [8, 6, 5, 1] [8, 7, 6, 1] [8, 7, 6, 5, 2, 1] [8, 6, 4, 3, 2, 1]
9	511	[9, 4] [9, 6, 4, 3] [9, 8, 5, 4] [9, 8, 4, 1] [9, 5, 3, 2] [9, 8, 6, 5] [9, 8, 7, 2] [9, 6, 5, 4, 2] [9, 7, 6, 4, 3, 1] [9, 8, 7, 6, 5, 3]
10	1023	[10, 3] [10, 8, 3, 2] [10, 4, 3, 1] [10, 8, 5, 1][10, 8, 5, 4] [10, 9, 4, 1] [10, 8, 4, 3] [10, 5, 3, 2] [10, 5, 2, 1] [10, 9, 4, 2]
11	2047	[11, 1] [11, 8, 5, 2] [11, 7, 3, 2] [11, 5, 3, 5] [11, 10, 3, 2] [11, 6, 5, 1] [11, 5, 3, 1] [11, 9, 4, 1] [11, 8, 6, 2] [11, 9, 8, 3]
12	4095	[12, 6, 4, 1] [12, 9, 3, 2] [12, 11, 10, 5, 2, 1] [12, 11, 6, 4, 2, 1] [12, 11, 9, 7, 6, 5] [12, 11, 9, 5, 3, 1] [12, 11, 9, 8, 7, 4] [12, 11, 9, 7, 6, 5] [12, 9, 8, 3, 2, 1] [12, 10, 9, 8, 6, 2]
13	8191	[13, 4, 3, 1] [13, 10, 9, 7, 5, 4] [13, 11, 8, 7, 4, 1] [13, 12, 8, 7, 6, 5] [13, 9, 8, 7, 5, 1] [13, 12, 6, 5, 4, 3] [13, 12, 11, 9, 5, 3] [13, 12, 11, 5, 2, 1] [13, 12, 9, 8, 4, 2] [13, 8, 7, 4, 3, 2]
14	16,383	[14, 12, 2, 1] [14, 13, 4, 2] [14, 13, 11, 9] [14, 10, 6, 1] [14, 11, 6, 1] [14, 12, 11, 1] [14, 6, 4, 2] [14, 11, 9, 6, 5, 2] [14, 13, 6, 5, 3, 1] [14, 13, 12, 8, 4, 1] [14, 8, 7, 6, 4, 2] [14, 10, 6, 5, 4, 1] [14, 13, 12, 7, 6, 3] [14, 13, 11, 10, 8, 3]
15	32,767	[15, 13, 10, 9] [15, 13, 10, 1] [15, 14, 9, 2] [15, 1] [15, 9, 4, 1] [15, 12, 3, 1] [15, 10, 5, 4] [15, 10, 5, 4, 3, 2] [15, 11, 7, 6, 2, 1] [15, 7, 6, 3, 2, 1] [15, 10, 9, 8, 5, 3] [15, 12, 5, 4, 3, 2] [15, 10, 9, 7, 5, 3] [15, 13, 12, 10] [15, 13, 10, 2] [15, 12, 9, 1] [15, 14, 12, 2] [15, 13, 9, 6] [15, 7, 4, 1] [15, 4] [15, 13, 7, 4]
16	65,535	[16, 12, 3, 1] [16, 12, 9, 6] [16, 9, 4, 3] [16, 12, 7, 2] [16, 10, 7, 6] [16, 15, 7, 2] [16, 9, 5, 2] [16, 13, 9, 6] [16, 15, 4, 2] [16, 15, 9, 4]
17	131,071	[17, 3] [17, 3, 2] [17, 7, 4, 3] [17, 16, 3, 1] [17, 12, 6, 3, 2, 1] [17, 8, 7, 6, 4, 3] [17, 11, 8, 6, 4, 2] [17, 9, 8, 6, 4, 1] [17, 16, 14, 10, 3, 2] [17, 12, 11, 8, 5, 2]
18	262, 143	[18, 7] [18, 10, 7, 5] [18, 13, 11, 9, 8, 7, 6, 3] [18, 17, 16, 15, 10, 9, 8, 7] [18, 15, 12, 11, 9, 8, 7, 6]
19	524,287	[19, 5, 2, 1] [19, 13, 8, 5, 4, 3] [19, 12, 10, 9, 7, 3] [19, 17, 15, 14, 13, 12, 6, 1] [19, 17, 15, 14, 13, 9, 8, 4, 2, 1] [19, 16, 13, 11, 19, 9, 4, 1] [19, 9, 8, 7, 6, 3] [19, 16, 15, 13, 12, 9, 5, 4, 2, 1] [19, 18, 15, 14, 11, 10, 8, 5, 3, 2] [19, 18, 17, 16, 12, 7, 6, 5, 3, 1]
20	1, 048,575	[20, 3] [20, 9, 5, 3] [20, 19, 4, 3] [20, 11, 8, 6, 3, 2] [20, 17, 14, 10, 7, 4, 3, 2]
21	2,097,151	[21, 2] [21, 14, 7, 2] [21, 13, 5, 2] [21, 14, 7, 6, 3, 2] [21, 8, 7, 4, 3, 2] [21, 10, 6, 4, 3, 2] [21, 15, 10, 9, 5, 4, 3, 2] [21, 14, 12, 7, 6, 4, 3, 2] [21, 20, 19, 18, 5, 4, 3, 2]
22	4,194,303	[22,1] [22, 9, 5, 1] [22, 20, 18, 16,6, 4, 2, 1] [22, 19, 16, 13, 10, 7, 4, 1] [22, 17, 9, 7, 2, 1] [22, 17, 13, 12, 8, 7, 2, 1] [22, 14, 13, 12, 7, 3, 2, 1]
23	8,388,607	[23, 5] [23, 17, 11, 5] [23, 5, 4, 1] [23, 12, 5, 4] [23, 21, 7, 5] [23, 16, 13, 6, 5, 3] [23, 11, 10, 7, 6, 5] [23, 15, 10, 9, 7, 5, 4, 3] [23, 17, 11, 9, 8, 5, 4, 1] [23, 18, 16, 13, 11, 8, 5, 2]
24	16,777,215	[24, 7, 2] [24, 4, 3, 1] [24, 22, 20, 18, 16, 14, 11, 9, 8, 7, 5, 4] [24, 21, 19, 18, 17, 16, 15, 14, 13, 10, 9, 5, 4, 1]
25	33,554, 431	[25, 3] [25, 3, 2, 1] [25, 20, 5, 3] [25, 12, 5, 4] [25, 17, 10, 3, 2, 1] [25, 23, 21, 19, 9, 7, 5, 3] [25, 18, 12, 11, 6, 5, 4] [25, 20, 16, 11, 5, 3, 2, 1] [25, 12, 11, 8, 7, 6, 4, 3]
26	67,108,863	[26, 6, 2, 1] [26, 22, 21, 16, 12, 11, 10, 8, 5, 4, 3, 1]
27	134,217,727	[27, 5, 2, 1] [27, 18, 11, 10, 9, 5, 4, 3]
28	268,435,455	[28, 3] [28, 13, 11, 9, 5, 3] [28, 22, 11, 10, 4, 3] [28, 24, 20, 16, 12, 8, 4, 3, 2, 1]
29	536,870,911	[29, 2] [29, 20, 11, 2] [29, 13, 7, 2] [29, 21, 5, 2] [29, 26, 5, 2] [29, 19, 16, 6, 3, 2] [29, 18, 14, 6, 3, 2]
30	1,073,741,823	[30, 23, 2, 1] [30, 6, 4, 1] [30, 24, 20, 16, 14, 13, 11, 7, 2, 1]
31	2,147,483,647	[31, 29, 21, 17] [31, 28, 19, 15] [31, 3] [31, 3, 2, 1] [31, 13, 8, 3] [31, 21, 12, 3, 2, 1] [31, 20, 18, 7, 5, 3] [31, 30, 29, 25] [31, 28, 24, 10] [31, 20, 15, 5, 4, 3] [31, 16, 8, 4, 3, 2]
32	4,294,967,295	[32, 22, 2, 1] [32, 7, 5, 3, 2, 1] [32, 28, 19, 18, 16, 14, 11, 10, 9, 6, 5, 1]
33	8,589,934,591	[33, 13] [33, 22, 13, 11] [33, 26, 14, 10] [33, 6, 4, 1] [33, 22, 16, 13, 11, 8]
61	2,305,843,009, 213, 693, 951	[61, 5, 2, 1]
89	618,970,019,642,690, 137,449,562,112	[89, 6, 5, 3]
Reprinted by permission of John Wiley & Sons. From Spread Spectrum Systems, 2nd edition, p. 87, Robert C. Dixon. Copyright © 1984 by John Wiley & Sons, Inc.

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ClockLFSR (Linear Feedback Shift Register)